MatrixExponential

From what I can gather, a linear space and a vector space are different terms for the exact same concept, but I'm looking for confirmation.

Also, I've read that a Hilbert space "is a vector space that possesses a dot product." I thought all vector spaces could eventually be derived to have a dot product. Can anyone give an example of a vector space that does not have a dot product? What are some of the practical uses for this sort of distinction?

I'm currently taking a graduate class that involves computer modeling of some engineering situations. Our professor is recommending that we use C or FORTRAN (barf). He insists that we need a compiled code, because we are going to get into some very large matrices (much larger than 256 by 256 is as descriptive as he's been) and interpreted languages like Matlab or Python take prohibitively long to crunch. He's told us some cautionary tales about students who ignored his advice and tried to write code in those two languages, and when push came to shove, they failed the class cause the couldn't get their code to run in a meaningful time frame. The thing is, while I'm familiar with text based

I am an agnostic atheist. My wife, father and best friend describe themselves as merely agnostic. By the strictest definition of these terms, I feel they should claim the moniker of "agnostic atheist" as well. Most of our discussions about the facts of the matter lead to much agreement.

My perspective, after listening to their reasons for keeping the agnostic part and dropping the atheist part, is that for most people in modern american society, the term atheist is seen as inflammatory and combative, whereas the term agnostic is accepted as fairly benign, open-minded, and generally acceptable.

What's more, these three important people in my life espouse the general view that when it com

So I've been playing minecraft for two whole weeks now (total noob) and from some of the videos I've watched it seems like RedPower2 is the mod I want to start with (only played vanilla MC so far).

I've been reading up on how to install Forge and mods but I'm left a little confused on all the tutorials (mostly because so far nothing has worked).

The only MC version I have downloaded (ever) is 1.7.4, and I've seen that in the launcher I can edit profiles to play previous versions. So since RP2 needs v1.4.6 I've made a profile for that.

Now when it comes to installing forge, all the videos say to install the "latest one", but I'm getting the feeling that's just cause the videos are old.

First, for the sake of argument, assume there is an omniscient being (mind, spirit, robot, God...whatever). Let's call it The Mind, for short (and to remove the argument slightly from other preconceived notions and properties one might typically attribute to God).

Now, by definition of omniscience, The Mind knows all things in every detail. Thus, all things exist within The Mind, in the form of information.

Now my first premise is that there is no (practical) distinction from these things existing within The Mind and existing outside of The Mind, since both entail the same level of detail, the same objects carrying out the same actions with the same consequences, etc.

Assuming the valid

Most religions take Free Will as a given and make it an unconcious cornerstone of their faith. For example, why does a perfect god allow sin to exist, why did he create satan, etc. etc. are typically explained away along the lines of "because free will is so important."

I have two, if not questions exactly, then points of discussion:

1. Modern information and artificial intelligence theories (particular those concerned with "agents") indicate that any useful "thinking" system would necessarily need to assume itself to have free will. That is, it creates a model of the universe in its head, including itself, then makes predictions inside the model about the effects various actions will h

I was raised a believer but am now a skeptic, and I have had issues wrapping my brain around the concept of faith since I was about 8.

I see faith as being distinctly different from trust. Trust seems to be based an a series of evidence, like if were to meet you, and you were nice to me every day for a week or so, I would trust that you are a nice person. My trust would grow stronger as time went on, and you consistently upheld my trust. Faith, on the other hand, is more like "the benefit of the doubt". The moment I meet you, I might have faith that you are a nice person, but I have no baseline for trust. In short, I define faith as trust without a baseline (or trust without proof or

I know many Christians who believe that parts of the Bible, Genesis in particular, are metaphorical. That it refers to the way things really happened, but does not depict them literally. In particular they accept big bang cosmology and evolutionary theory as not conflicting with the Genesis creation story, as the latter is merely a poetic description of the former, not a scientific one.

My question is, if you are not a Fundamentalist, and you accept that some portions of the Bible are not literal, then where do you draw the line? How do you arrive at this conclusion? What sources inform this decision?

If the 7 days are a metaphor for millions or billions of years, then perhaps Jesus of

The Old Testament is riddled with cleanliness laws, from what not to eat, to how to handle the sick, to what should be done with items or people who touch something unclean (such as an animal carcass).

Why then is there no mention of sterilization through immersion in boiling water? It is not as if it is an advanced concept, or that the ancient Hebrews lacked the equipment necessary (fire, water, pots). They wouldn't even need to know why they were required to do such a thing (just as other cleanliness laws give no explanation beyond "unclean"). If these are really inspired rules, and not rules based on observation, then why would the inspirer not bother to mention such a simple and effe

This is a poem I wrote when I was younger and thought you guys might appreciate, considering the lack of secular humanist poetry (at least as far as I know)

The fall of forever

Down these halls of burning nether,

Oh this dream that we sinned and fell from grace.

Is a vain and empty sorrow

The mute voice we sought to borrow

From somewhere beyond the heart of our weak race


But this power we would possess

One wakes to find is nothing less

Than a power never truly to be had.

Built to free us from the chains

And alleviate the pains

From a war with a world gone mad.


All we know must burn away

And so we turn to fall, a